Factor graph is an efficient representation in that it captures sparsity among variables: two variables are independent of each other given all other variables if and only if they do not belong to the same factor.
The log likelihood, \(\log p(x)\) , can be written in a sum of factors:
\(\log p(x) \propto \sum _{a\in \mathcal {A}} \phi _a \left(x_{\lbrace a\rbrace } \right)\) ,
where \(\mathcal {A}\)  is the set of all factors. Each factor \(\phi _a(x_{\lbrace a\rbrace })\)  maps the values of random variables to a strictly positive real number representing the log likelihood of the variables.
With graphical models, there exist fast algorithms to compute statistical properties such as marginalization, expectation, maximum likelihood [1]}.
<FIGURE>